It sounds like this child is way over the top in terms of transitioning.
Transitioning usually means crying and being scared to move even 2 inches from your clutches until they feel comfy with the surroundings and get used to routines. Other transitioning things are constantly wanting to be carried and just being unable to play independently for even 30 seconds.

Vomit is where I draw the line every time. If a kid would cry to that point then I would head for the hills. Vomit is just so gross and extreme that it is a red flag

Are there other people who you could interview and give the spot to? This child may take a loooong time to transition and I would be scared that the behaviour might not improve before your trial period is up and then it is harder to get rid of them.

Good luck though. I feel for you !!